State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis

(ii) The set of letters in the English alphabet

(iii) The set of numbers which are multiple of 5

(iv) The set of animals living on the earth

(v) The set of circles passing through the origin (0, 0)

Asked by Pragya Singh | 11 months ago |  69

##### Solution :-

(i) Given that,

The set of lines which are parallel to x axis

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

The lines parallel to x axes are infinite in number.

The set of line parallel to x axis is infinite.

(ii) Given that,

The set of letter sin English alphabet

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

English alphabet consist of 26 elements which is finite in number

The set of letters in the English alphabet is finite.

(iii) Given that,

The set of numbers which are multiple of 5

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

The numbers which are all multiple of 5 are infinite in number.

The set of numbers which are multiple of 5 is infinite.

(iv) Given that,

The set of animals living on the earth

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

Although the number of animals on the earth is quite a big number, it is finite.

The set of animals living on the earth is finite.

(v) Given that,

The set of circles passing through the origin (0,0)

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

The number of circles passing through the origin may be infinite in number.

The set of circles passing through origin (0,0) is infinite.

Answered by Abhisek | 11 months ago

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